Please use this identifier to cite or link to this item: http://hdl.handle.net/2381/44772
Title: Contravariant form on tensor product of highest weight modules
Authors: Mudrov, Andrey I.
First Published: 7-Apr-2019
Publisher: National Academy of Science of Ukraine
Citation: Symmetry, Integrability and Geometry : Methods and Applications, 2019, 15 (026), pp. ?-? (10)
Abstract: We give a criterion for complete reducibility of tensor product V ⊗ Z of two irreducible highest weight modules V and Z over a classical or quantum semi-simple group in terms of a contravariant symmetric bilinear form on V ⊗ Z. This form is the product of the canonical contravariant forms on V and Z. Then V ⊗ Z is completely reducible if and only if the form is non-degenerate when restricted to the sum of all highest weight submodules in V ⊗ Z or equivalently to the span of singular vectors.
DOI Link: 10.3842/SIGMA.2019.026
ISSN: 1815-0659
Links: https://www.emis.de/journals/SIGMA/2019/026/
http://hdl.handle.net/2381/44772
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © the authors, 2019. This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike License (https://creativecommons.org/licenses/by-sa/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited, and that any contributions are distributed under the same license as the original.
Description: 2010 Mathematics Subject Classification: 17B10; 17B37
Appears in Collections:Published Articles, Dept. of Mathematics

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